Optimizing news headlines is important for publishers and media sites. A compelling headline will increase readership, user engagement and social shares. At Yahoo Front Page, headline testing is carried out using a test-rollout strategy: we first allocate equal proportion of the traffic to each headline variation for a defined testing period, and then shift all future traffic to the best-performing variation. In this paper, we introduce a multi-armed bandit (MAB) approach with batched Thompson Sampling (bTS) to dynamically test headlines for news articles. This method is able to gradually allocate traffic towards optimal headlines while testing. We evaluate the bTS method based on empirical impressions/clicks data and simulated user responses. The result shows that the bTS method is robust, converges accurately and quickly to the optimal headline, and outperforms the test-rollout strategy by 3.69% in terms of clicks.
In this paper, we study the multi-armed bandit problem in the batched setting where the employed policy must split data into a small number of batches. While the minimax regret for the two-armed stochastic bandits has been completely characterized in \cite{perchet2016batched}, the effect of the number of arms on the regret for the multi-armed case is still open. Moreover, the question whether adaptively chosen batch sizes will help to reduce the regret also remains underexplored. In this paper, we propose the BaSE (batched successive elimination) policy to achieve the rate-optimal regrets (wit…
We study Thompson Sampling algorithms for stochastic multi-armed bandits in the batched setting, in which we want to minimize the regret over a sequence of arm pulls using a small number of policy changes (or, batches). We propose two algorithms and demonstrate their effectiveness by experiments on both synthetic and real datasets. We also analyze the proposed algorithms from the theoretical aspect and obtain almost tight regret-batches tradeoffs for the two-arm case.
We study the asymptotic performance of the Thompson sampling algorithm in the batched multi-armed bandit setting where the time horizon $T$ is divided into batches, and the agent is not able to observe the rewards of her actions until the end of each batch. We show that in this batched setting, Thompson sampling achieves the same asymptotic performance as in the case where instantaneous feedback is available after each action, provided that the batch sizes increase subexponentially. This result implies that Thompson sampling can maintain its performance even if it receives delayed feedback in …
We study the $K$-armed dueling bandit problem, a variation of the traditional multi-armed bandit problem in which feedback is obtained in the form of pairwise comparisons. Previous learning algorithms have focused on the $\textit{fully adaptive}$ setting, where the algorithm can make updates after every comparison. The "batched" dueling bandit problem is motivated by large-scale applications like web search ranking and recommendation systems, where performing sequential updates may be infeasible. In this work, we ask: $\textit{is there a solution using only a few adaptive rounds that matches t…
Columbia University（哥伦比亚大学）；University of Michigan（密歇根大学）
The $K$-armed dueling bandit problem, where the feedback is in the form of noisy pairwise comparisons, has been widely studied. Previous works have only focused on the sequential setting where the policy adapts after every comparison. However, in many applications such as search ranking and recommendation systems, it is preferable to perform comparisons in a limited number of parallel batches. We study the batched $K$-armed dueling bandit problem under two standard settings: (i) existence of a Condorcet winner, and (ii) strong stochastic transitivity and stochastic triangle inequality. For bot…
Batched Single-Index Global Multi-Armed Bandits with Covariates
Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University（数学系、应用数学与统计学系，凯斯西储大学）；Department of Statistics, Pennsylvania State University（统计系，宾夕法尼亚州立大学）
National University of Singapore（新加坡国立大学）；University of California, Los Angeles（加州大学洛杉矶分校）
We study the multi-armed bandit problem with subgaussian rewards. The explore-then-commit (ETC) strategy, which consists of an exploration phase followed by an exploitation phase, is one of the most widely used algorithms in a variety of online decision applications. Nevertheless, it has been shown in Garivier et al. (2016) that ETC is suboptimal in the asymptotic sense as the horizon grows, and thus, is worse than fully sequential strategies such as Upper Confidence Bound (UCB). In this paper, we show that a variant of ETC algorithm can actually achieve the asymptotic optimality for multi-arm…
University of Virginia（弗吉尼亚大学）；The Hong Kong University of Science and Technology（香港科技大学）；The Pennsylvania State University（宾夕法尼亚州立大学）
Despite the significant interests and many progresses in decentralized multi-player multi-armed bandits (MP-MAB) problems in recent years, the regret gap to the natural centralized lower bound in the heterogeneous MP-MAB setting remains open. In this paper, we propose BEACON -- Batched Exploration with Adaptive COmmunicatioN -- that closes this gap. BEACON accomplishes this goal with novel contributions in implicit communication and efficient exploration. For the former, we propose a novel adaptive differential communication (ADC) design that significantly improves the implicit communication e…
In many public health settings, there is a perceived tension between allocating resources to known vulnerable areas and learning about the overall prevalence of the problem. Inspired by a door-to-door Covid-19 testing program we helped design, we combine multi-armed bandit strategies and insights from sampling theory to demonstrate how to recover accurate prevalence estimates while continuing to allocate resources to at-risk areas. We use the outbreak of an infectious disease as our running example. The public health setting has several characteristics distinguishing it from typical bandit set…
We introduce a novel anytime Batched Thompson sampling policy for multi-armed bandits where the agent observes the rewards of her actions and adjusts her policy only at the end of a small number of batches. We show that this policy simultaneously achieves a problem dependent regret of order $O(\log(T))$ and a minimax regret of order $O(\sqrt{T\log(T)})$ while the number of batches can be bounded by $O(\log(T))$ independent of the problem instance over a time horizon $T$. We also show that in expectation the number of batches used by our policy can be bounded by an instance dependent bound of o…
Microsoft Research（微软研究院）；Sorbonne Université（索邦大学）；Orange Labs（法国电信实验室）
In Batched Multi-Armed Bandits (BMAB), the policy is not allowed to be updated at each time step. Usually, the setting asserts a maximum number of allowed policy updates and the algorithm schedules them so that to minimize the expected regret. In this paper, we describe a novel setting for BMAB, with the following twist: the timing of the policy update is not controlled by the BMAB algorithm, but instead the amount of data received during each batch, called \textit{crowd}, is influenced by the past selection of arms. We first design a near-optimal policy with approximate knowledge of the param…
Continuum-armed Bandit Optimization with Batch Pairwise Comparison Oracles
Department of Information Systems and Intelligence Business, Xi’an Jiaotong University, Xi’an 710049, China（西安交通大学信息系统与智能商业系）；Stern School of Business, New York University, New York, NY 10012, USA（纽约大学斯特恩商学院）；Naveen Jindal School of Management, University of Texas at Dallas, Richardson, TX 75080, USA（德克萨斯大学达拉斯分校奈维恩·金达管理学院）
Google Research（谷歌研究院）；Yale University（耶鲁大学）；McGill University（麦吉尔大学）
We present simple and efficient algorithms for the batched stochastic multi-armed bandit and batched stochastic linear bandit problems. We prove bounds for their expected regrets that improve over the best-known regret bounds for any number of batches. In particular, our algorithms in both settings achieve the optimal expected regrets by using only a logarithmic number of batches. We also study the batched adversarial multi-armed bandit problem for the first time and find the optimal regret, up to logarithmic factors, of any algorithm with predetermined batch sizes.
The Impact of Batch Learning in Stochastic Linear Bandits
Eindhoven University of Technology（埃因霍温理工大学）；Jheronimus Academy of Data Science（赫罗尼姆斯数据科学学院）；Tilburg University（蒂尔堡大学）；University of Jyväskylä（于韦斯屈莱大学）
